Polygon Filling & Antialiasing - Computer Science - Worcester ...
Computer Graphics CS 543 Lecture 11 (Part 1) Polygon Filling & Antialiasing Prof Emmanuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI)
Defining and Filling Regions of Pixels
Methods of defining region
Pixel‐defined: specifies pixels in color or geometric range Symbolic: provides property pixels in region must have Examples of symbolic:
Closeness to some pixel Within circle of radius R Within a specified polygon
Pixel‐Defined Regions
Definition: Region R is the set of all pixels having color C that are connected to a given pixel S 4‐adjacent: pixels that lie next to each other horizontally or vertically, NOT diagonally 8‐adjacent: pixels that lie next to each other horizontally, vertically OR diagonally 4‐connected: if there is unbroken path of 4‐adjacent pixels connecting them 8‐connected: unbroken path of 8‐adjacent pixels connecting them
Recursive Flood‐Fill Algorithm
Recursive algorithm Starts from initial pixel of color, intColor Recursively set 4‐connected neighbors to newColor Flood‐Fill: floods region with newColor Basic idea:
start at “seed” pixel (x, y) If (x, y) has color intColor, change it to newColor Do same recursively for all 4 neighbors
Recursive Flood‐Fill Algorithm
Note: getPixel(x,y) used to interrogate pixel color at (x, y)
void floodFill(short x, short y, short intColor) { if(getPixel(x, y) == intColor) { setPixel(x, y); floodFill(x – 1, y, intColor); // left pixel floodFill(x + 1, y, intColor); // right pixel floodFill(x, y + 1, intColor); // down pixel floodFill(x, y – 1, intColor); // up pixel } }
(x, y+1)
(x-1, y (x, y) (x, y-1)
(x+1, y)
Recursive Flood‐Fill Algorithm
Recursive flood‐fill is blind Some pixels retested several times Region coherence is likelihood that an interior pixel mostly likely adjacent to another interior pixel Coherence can be used to improve algorithm performance A run: group of adjacent pixels lying on same scanline Fill runs(adjacent, on same scan line) of pixels
Region Filling Using Coherence
Example: start at s, initial seed
Pseudocode: Push address of seed pixel onto stack while(stack is not empty) { Pop stack to provide next seed Fill in run defined by seed In row above find reachable interior runs Push address of their rightmost pixels Do same for row below current run }
Note: algorithm most efficient if there is span coherence (pixels on scanline have same value) and scan-line coherence (consecutive scanlines similar)
Filling Polygon‐Defined Regions
Problem: Region defined polygon with vertices Pi = (Xi, Yi), for i = 1…N, specifying sequence of P’s vertices P2
P1 P7
P3
P5 P6
P4
Filling Polygon‐Defined Regions
Solution: Progress through frame buffer scan line by scan line, filling in appropriate portions of each line Filled portions defined by intersection of scan line and polygon edges Runs lying between edges inside P are filled Pseudocode:
for(each scan Line L) { Find intersections of L with all edges of P Sort the intersections by increasing x-value Fill pixel runs between all pairs of intersections }
Filling Polygon‐Defined Regions
Example: scan line y = 3 intersects 4 edges e3, e4, e5, e6 Sort x values of intersections and fill runs in pairs Note: at each intersection, inside‐outside (parity), or vice versa P2
P1 P7
P3
e6
e3 P5
3 P6
e5
e4
P4
Data Structure
Filling Polygon‐Defined Regions
Problem: What if two polygons A, B share an edge? Algorithm behavior could result in: setting edge first in one color and the another Drawing edge twice too bright Make Rule: when two polygons share edge, each polygon owns its left and bottom edges E.g. below draw shared edge with color of polygon B B A
Filling Polygon‐Defined Regions
Problem: How to handle cases where scan line intersects with polygon endpoints to avoid wrong parity? Solution: Discard intersections with horizontal edges and with upper endpoint of any edge See 0
See 0
See 2
See 0 See 2
See 1
See 1
Antialiasing
Raster displays have pixels as rectangles Aliasing: Discrete nature of pixels introduces “jaggies”
Antialiasing
Aliasing effects:
Distant objects may disappear entirely Objects can blink on and off in animations
Antialiasing techniques involve some form of blurring to reduce contrast, smoothen image Three antialiasing techniques:
Prefiltering Postfiltering Supersampling
Prefiltering
Basic idea:
Example: if polygon covers ¼ of the pixel
compute area of polygon coverage use proportional intensity value Pixel color = ¼ polygon color + ¾ adjacent region color
Cons: computing polygon coverage can be time consuming
Supersampling
Assumes we can compute color of any location (x,y) on screen Increase frequency of sampling Instead of (x,y) samples in increments of 1 Sample (x,y) in fractional (e.g. ½) increments, average samples Example: Double sampling = increments of ½ = 9 color values averaged for each pixel
Average 9 (x, y) values to find pixel color
Postfiltering
Supersampling uses average Gives all samples equal importance Post‐filtering: use weighting (different levels of importance) Compute pixel value as weighted average Samples close to pixel center given more weight Sample weighting
1/16
1/16
1/16
1/2
1/16
1/16
1/16 1/16 1/16
Antialiasing in OpenGL
Many alternatives Simplest: accumulation buffer Accumulation buffer: extra storage, similar to frame buffer Samples are accumulated When all slightly perturbed samples are done, copy results to frame buffer and draw
Antialiasing in OpenGL
First initialize: glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB | GLUT_ACCUM | GLUT_DEPTH); Zero out accumulation buffer glClear(GLUT_ACCUM_BUFFER_BIT); Add samples to accumulation buffer using glAccum( )
Antialiasing in OpenGL
Sample code jitter[] stores randomized slight displacements of camera, factor, f controls amount of overall sliding
glClear(GL_ACCUM_BUFFER_BIT); for(int i=0;i < 8; i++) { cam.slide(f*jitter[i], f*jitter[i].y, 0); display( ); jitter.h glAccum(GL_ACCUM, 1/8.0); } -0.3348, 0.4353 glAccum(GL_RETURN, 1.0); 0.2864, -0.3934 ……
References
Hill and Kelley, chapter 11 Angel and Shreiner, Interactive Computer Graphics, 6th edition
Defining and Filling Regions of Pixels
Methods of defining region
Pixel‐defined: specifies pixels in color or geometric range Symbolic: provides property pixels in region must have Examples of symbolic:
Closeness to some pixel Within circle of radius R Within a specified polygon
Pixel‐Defined Regions
Definition: Region R is the set of all pixels having color C that are connected to a given pixel S 4‐adjacent: pixels that lie next to each other horizontally or vertically, NOT diagonally 8‐adjacent: pixels that lie next to each other horizontally, vertically OR diagonally 4‐connected: if there is unbroken path of 4‐adjacent pixels connecting them 8‐connected: unbroken path of 8‐adjacent pixels connecting them
Recursive Flood‐Fill Algorithm
Recursive algorithm Starts from initial pixel of color, intColor Recursively set 4‐connected neighbors to newColor Flood‐Fill: floods region with newColor Basic idea:
start at “seed” pixel (x, y) If (x, y) has color intColor, change it to newColor Do same recursively for all 4 neighbors
Recursive Flood‐Fill Algorithm
Note: getPixel(x,y) used to interrogate pixel color at (x, y)
void floodFill(short x, short y, short intColor) { if(getPixel(x, y) == intColor) { setPixel(x, y); floodFill(x – 1, y, intColor); // left pixel floodFill(x + 1, y, intColor); // right pixel floodFill(x, y + 1, intColor); // down pixel floodFill(x, y – 1, intColor); // up pixel } }
(x, y+1)
(x-1, y (x, y) (x, y-1)
(x+1, y)
Recursive Flood‐Fill Algorithm
Recursive flood‐fill is blind Some pixels retested several times Region coherence is likelihood that an interior pixel mostly likely adjacent to another interior pixel Coherence can be used to improve algorithm performance A run: group of adjacent pixels lying on same scanline Fill runs(adjacent, on same scan line) of pixels
Region Filling Using Coherence
Example: start at s, initial seed
Pseudocode: Push address of seed pixel onto stack while(stack is not empty) { Pop stack to provide next seed Fill in run defined by seed In row above find reachable interior runs Push address of their rightmost pixels Do same for row below current run }
Note: algorithm most efficient if there is span coherence (pixels on scanline have same value) and scan-line coherence (consecutive scanlines similar)
Filling Polygon‐Defined Regions
Problem: Region defined polygon with vertices Pi = (Xi, Yi), for i = 1…N, specifying sequence of P’s vertices P2
P1 P7
P3
P5 P6
P4
Filling Polygon‐Defined Regions
Solution: Progress through frame buffer scan line by scan line, filling in appropriate portions of each line Filled portions defined by intersection of scan line and polygon edges Runs lying between edges inside P are filled Pseudocode:
for(each scan Line L) { Find intersections of L with all edges of P Sort the intersections by increasing x-value Fill pixel runs between all pairs of intersections }
Filling Polygon‐Defined Regions
Example: scan line y = 3 intersects 4 edges e3, e4, e5, e6 Sort x values of intersections and fill runs in pairs Note: at each intersection, inside‐outside (parity), or vice versa P2
P1 P7
P3
e6
e3 P5
3 P6
e5
e4
P4
Data Structure
Filling Polygon‐Defined Regions
Problem: What if two polygons A, B share an edge? Algorithm behavior could result in: setting edge first in one color and the another Drawing edge twice too bright Make Rule: when two polygons share edge, each polygon owns its left and bottom edges E.g. below draw shared edge with color of polygon B B A
Filling Polygon‐Defined Regions
Problem: How to handle cases where scan line intersects with polygon endpoints to avoid wrong parity? Solution: Discard intersections with horizontal edges and with upper endpoint of any edge See 0
See 0
See 2
See 0 See 2
See 1
See 1
Antialiasing
Raster displays have pixels as rectangles Aliasing: Discrete nature of pixels introduces “jaggies”
Antialiasing
Aliasing effects:
Distant objects may disappear entirely Objects can blink on and off in animations
Antialiasing techniques involve some form of blurring to reduce contrast, smoothen image Three antialiasing techniques:
Prefiltering Postfiltering Supersampling
Prefiltering
Basic idea:
Example: if polygon covers ¼ of the pixel
compute area of polygon coverage use proportional intensity value Pixel color = ¼ polygon color + ¾ adjacent region color
Cons: computing polygon coverage can be time consuming
Supersampling
Assumes we can compute color of any location (x,y) on screen Increase frequency of sampling Instead of (x,y) samples in increments of 1 Sample (x,y) in fractional (e.g. ½) increments, average samples Example: Double sampling = increments of ½ = 9 color values averaged for each pixel
Average 9 (x, y) values to find pixel color
Postfiltering
Supersampling uses average Gives all samples equal importance Post‐filtering: use weighting (different levels of importance) Compute pixel value as weighted average Samples close to pixel center given more weight Sample weighting
1/16
1/16
1/16
1/2
1/16
1/16
1/16 1/16 1/16
Antialiasing in OpenGL
Many alternatives Simplest: accumulation buffer Accumulation buffer: extra storage, similar to frame buffer Samples are accumulated When all slightly perturbed samples are done, copy results to frame buffer and draw
Antialiasing in OpenGL
First initialize: glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB | GLUT_ACCUM | GLUT_DEPTH); Zero out accumulation buffer glClear(GLUT_ACCUM_BUFFER_BIT); Add samples to accumulation buffer using glAccum( )
Antialiasing in OpenGL
Sample code jitter[] stores randomized slight displacements of camera, factor, f controls amount of overall sliding
glClear(GL_ACCUM_BUFFER_BIT); for(int i=0;i < 8; i++) { cam.slide(f*jitter[i], f*jitter[i].y, 0); display( ); jitter.h glAccum(GL_ACCUM, 1/8.0); } -0.3348, 0.4353 glAccum(GL_RETURN, 1.0); 0.2864, -0.3934 ……
References
Hill and Kelley, chapter 11 Angel and Shreiner, Interactive Computer Graphics, 6th edition
